The present invention generally pertains to the production of ultrafine particles and fibers and is particularly directed to the production of ultrafine particles and fibers of a given material by evaporating and condensing the material in an atmosphere of inert gas.
Ultrafine particles are defined herein as particles having characteristic dimensions of from 10 angstroms to 1 micron. The present invention is focused on the production of ultrafine particles in the range of from 100 to 1000 angstroms.
Ultrafine fibers are defined herein as fibers having diameters in the same range, from 100 to 1000 angstroms, and lengths at least three times longer than their diameters.
Ultrafine particles and ultrafine fibers have several unique features that make them particularly attractive for many applications. These features include (a) large surface area per unit volume, (b) at least one very small dimension, and (c) many boundaries per unit volume.
For example, 100 angstrom particles have a very large specific surface area of 600 m.sup.2 /cc. Thus, particles having a dimension as small as 100 angstroms have very rapid response in chemical diffusion reactions (fast kinetics) and to thermal stimuli (fast thermal response times). Also 100 angstrom particles can provide of order of 10.sup.6 boundaries (interfaces) per linear cm of length and thus produce matter in a very heterogeneous state.
Techniques for preparing ultrafine particles and ultrafine fibers by an evaporation and condensation process are described in the following publications:
Kimoto et al., "An Electron Microscope Study on Fine Metal Particles Prepared by Evaporation in Argon Gas at Low Pressure", Japan. J. Appl. Phys., Vol. 2, No. 11, Nov. 1963, pp. 702-713.
Tasaki et al, "Magnetic Properties of Ferromagnetic Metal Fine Particles Prepared by Evaporation in Argon Gas", Japan. J. Appl. Phys., Vol. 4, No. 10, Oct. 1965, pp. 707-711.
Kimoto and Nishida, "An Electron Microscope and Electron Diffraction Study of Fine Smoke Particles Prepared by Evaporation in Argon Gas at Low Pressures (II)", Japan. J. Appl. Phys., Vol. 6, No. 9, Sept. 1967, pp. 1047-1059.
Yatsuya et al., "Formation of Ultrafine Metal Particles by Gas Evaporation Technique. I. Aluminum in Helium", Japan. J. Appl. Phys., Vol. 12, No. 11, Nov. 1973, pp. 1675-1684.
Wada and Ichikawa, "A Method of Preparation of Finely Dispersed Ultrafine Particles", Japan. J. Appl. Phys., Vol. 15, No. 5, May 1976, p. 755-756.
Kato, "Preparation of Ultrafine Particles of Refractory Oxides by Gas-Evaporation Method", Japan. J. Appl. Phys., Vol. 15, No. 5, May 1976, pp. 757-760.
Granqvist and Buhrman, "Ultrafine Metal Particles", J. Appl. Phys., Vol. 47, No. 5, May 1976, pp. 2200-2219.
Kaito et al., "Growth of CdS Smoke Particles Prepared by Evaporation in Inert Gases", J. Appl. Phys., Vol. 47, No. 12, Dec. 1976, pp. 5161-5166.
Hayashi et al., "Formation of Ultrafine Metal Particles by Gas-Evaporation Technique. IV. Crystal Habits of Iron and Fcc Metals, Al, Co, Ni, Cu, Pd, Ag, In, Au and Pb", Japan. J. Appl. Phys., Vol. 16, No. 5, May 1977, pp. 705-717.
Kaito "Coalescence Growth of Smoke Particles Prepared by a Gas-Evaporation Technique", Japan. J. Appl. Phys., Vol. 17, No. 4, April 1978, pp. 601-609.
Shiojiri et al., "Coalescence Growth of Metal Smoke Particles Prepared by Gas Evaporation", J. Crystal Growth, Vol. 52, 1981, pp. 168-172.
Ando and Uyeda, "Preparation of Ultrafine Particles of Refractory Metal Carbides by a Gas-Evaporation Method", J. Crystal Growth, Vol. 52, 1981, pp. 178-181.
The technique used in the present invention is that of evaporation of material into an inert gas. Condensation ensues when the evaporated material expands into the inert gas and is cooled by the gas. A reactive gas may be mixed with the inert gas in order to alter the composition of the condensed material. Condensation can be divided into a three step process. First the expanding vapor becomes supersaturated and very small embryos condense in the vapor. Then the embryos grow into larger particles by additional vapor diffusing through the inert gas and condensing onto the embryos. Last, the particles collide and coalesce into larger particles. The coalescence rate depends on the particle density.
Resistively heated evaporation sources are commercially available in several refractory metals, principally tungsten (W), molybdenum (Mo), and tantalum (Ta). Some heaters are also available with either a refractory oxide coating or with a non-metallic crucible.
Condensation includes all of the particle growth processes that take place between the initial stages of condensation from vapor and the final collection of the particles. It is useful to divide the growth processes into three distinct stages: (a) embryo formation (the smallest particles), (b) diffusion of vapor to particles, and (c) particle coalescence. Embryo formation and accretion of vapor by particles are not strictly distinct stages. Particle coalescence is believed to be more distinct from the others.
Collection of particles is the final step. Convection insures that particles are moved rapidly over large distances in the experimental apparatus. Eventually they adhere to surfaces, making their collection easy.
It is useful to set the scale of important physical parameters under typical conditions. Set forth below are the parameters for an example using helium (He) as an inert gas and palladium (Pd) as the evaporated material condensing into 100 angstrom particles. The source temperature is taken to be 2000 K where Pd has a vapor pressure of 1 torr. All quantities refer to 2000 K and a He pressure of 10 torr. The gas is assumed to be an ideal Maxwell gas and the Pd particles are assumed to in the free molecular regime because they have Knudsen numbers, Kn, that are greater than 10.
______________________________________ Inert Gas Particles ______________________________________ P = 10 torr P (vapor) = 1 torr T = 2000K T = 2000K d = particle diameter = 100 angstroms Ng = gas density Np = particle density = 5 .times. 10.sup.16 /cm.sup.3 = 1 .times. 10.sup.11 /cm.sup.3 Vg = gas mean speed Vp = particle mean speed 3 .times. 10.sup.5 cm/s = 4 .times. 10.sup.2 cm/s Lg = gas mean free path Lp = particle apparent mfp = 1 .times. 10.sup.-2 cm = 1 .times. 10.sup.-2 cm Dg = gas diffusion coeff. Dp = particle diffusion coeff. = 4 .times. 10.sup.3 cm.sup.2 /s = 2 cm.sup.2 /s Kn = 2 .times. Lg/d = 2 .times. 10.sup.4 ______________________________________
Because of the higher temperatures and lower pressures, these diffusion coefficients and mean free paths are larger than usually encountered.
Embryos form very close to the source because of the large temperature gradients. For the example of Pd evaporation at 2000 K, it is calculated that the vapor need only be cooled by 29 K in order to be supersaturated by 30% (Sp=1.3). This temperature drop takes place within a few tenths of a mm of the source without convection. With convection it is not possible to make as general a statement, however it seems likely that there are still strong temperature gradients near the source.
Once embryos are formed with greater than a critical radius, R*, it is energetically favorable for them to grow. The ensuing growth of embryos and the birth of new ones has been analyzed in a publication by Dunning, "Nucleation, Growth, Ripening and Coagulation in Aerosol Formation", Symposia of the Faraday Society, No. 7, p. 7 (1973).
Following Dunning, imagine that at time zero there is a vapor which is out of equilibrium and free of any nuclei. The first generation of embryos are then born. Here we do not consider nucleation kinetics except to note that when the system is far from equilibrium they are rapid and become slow near equilibrium as Sp.perspectiveto.1.
First-born embryos grow by the diffusion and accretion of vapor and second generation embryos are then born. The radius of the first born embroyos grows as a function of time.
As the existing embryos grow, they deplete the system of vapor and thus R* increases. With increasing R*, the birth-rate of new embryos (the number born per unit time), diminishes.
Eventually, the birthrate becomes very small. The older generation embryos continue to accrete vapor, however, thereby increasing R*. Younger embryos can then have radii smaller than R*, and must begin to evaporate.
The single particle processes leading up this point produce a distribution of particle sizes even though the particles are assumed to be born with a very narrow range of sizes. However, the distribution decreases monotonically from a maximum size in contradistinction to what is observed. What is observed is a broad distribution with a tail extending to large sizes. This is due to the process of two or more particles coalescing, as discussed below.
It is observed that the particle distribution in many systems has a long tail extending to large sizes. This is true of numerous types of systems including aerosols and fine particles produced by the evaporation and condensation in inert gas technique. Frequently, the observed distributions are found not to be Gaussian in particle size but to be better represented by a lognormal distribution which is Gaussian in the logarithm of the particle size, as in publications by Fuchs and Sutugin, "Aerosol Science", Academic Press, p. 1 (1966), and Granqvist and Buhrman, J. Appl. Phys. Vol. 47, p. 2200 (1976).
Granqvist and Buhrman describe a lognormal distribution of fine particles of aluminum (Al) condensed in an argon (Ar) and oxygen (0.sub.2) atmosphere. The addition of 0.sub.2 is thought to lead to smaller particles. 0.sub.2 does, however, produce an oxide layer on the particles. The presence of the oxide layer does not appear to affect the lognormal distribution.
There is also a large spatial inhomogeneity in particle size due to convection.
Yatsuya et al., "Formation of Ultrafine Metal Particles by Gas Evaporation Technque. I. Aluminum in Helium", Japanese J. Appl. Phys. Vol 12, p. 1675 (1973) describe the variation of particle size distribution within a work chamber for evaporating and condensing ultrafinefine particles in an inert gas. Such variation is dominated by convective processes. Visually a convecting plume of particles is quite inhomogeneous, containing one or more dark bands and exhibiting changes with time.
The major point to be inferred from Yatsuya et al. is that there is a spatial variation of matter density within a plume. It is believed that this variation exists in part because the particle number density is strongly varying within the plume.
Smoluchowski (Phys. Z., Vol. 17, pp. 557 et. seq., 585 et. seq. (1916); Z. Phys. Chem., Vol. 92, p. 129 (1918)) was among the first to examine the coalescence or coagulation rate in a system of particles. He found that for a system of N identical particles per unit volume the time rate of change of particle density is EQU dN/dt=-K.sub.o N.sup.2 ( 1)
K.sub.o is a coagulation coefficient so that N decreases with time. It is significant that the rate of decrease is proportional to N squared.
Hidy and Brock teach that when there is a distribution of particle sizes then the net rate of change of the number of particles of size N.sub.k is equal to the sum of a creation term and a destruction term. ##EQU1## Care must be taken in equation 2 not to count events twice etc. The destruction term above causes the exhaustion of the smallest particles in order to produce larger ones. In addition, note that the time rate of change of particle number within a distribution varies as N squared.
Even if the initial particle distribution were monodisperse, the collisions within a plume, described by Yatsuya et al. leads to a dispersion in particle size by coalescence.
Any process which produces a relative velocity between particles contributes to coalescence due to particle-particle collisions. Some important processes are: (a) thermal diffusion (b) laminar and turbulent flow fields (c) electric and magnetic forces (d) gravitational and centrifugal force fields, and (e) others.
Thermal diffusion of particles is important because it is always present. It leads to a binary collision rate density, L.sub.ij between particles of Mass M.sub.i and M.sub.j given by EQU L.sub.ij =C.sub.ij .sqroot.(8piKT(1/M.sub.i +1/M.sub.j))R.sub.ij.sup.2 N.sub.i N.sub.j ( 3)
Hidy and Brock, "The Dynamics of Aerocolloidal Systems", Pergamon Press (1970).
C.sub.ij is either 1/2 or 1, K is Boltzmann's constant and R.sub.ij is the collision radius of interaction. L.sub.ij can be related to the coalescence rate by making assumptions about sticking coefficients. From equation 3, it is noted that (i) larger particles are relatively more important because of R.sub.ij, and that (ii) the rate is proportional to N.sub.i N.sub.j.
Laminar and turbulent flow fields cause particles to collide because of shear in the velocity fields. Electric and magnetic forces give a relative velocity between particles if the particles have opposite charges, induced dipole moments or intrinsic magnetic moments, as examples among many possibilities. Gravitational and centrifugal force fields cause collisions because heavier particles settle out faster.
The effects of coalescence within a convecting plume are more severe than the above remarks would indicate. FIG. 1 shows a qualitative sketch of the flow lines within a convecting plume.
Initially, evaporated material leaves the source 10 in a 4 pi solid angle, as sketched in FIG. 1. It is assumed that evaporated material condenses into particles within a few mm of the source, more rapidly at the bottom and more slowly at the top due to convection. The convecting inert gas flow rises from below, however, and "folds" up the evaporated and condensed material into a rising plume of particles and heated inert gas, much like a candle flame. In addition, some particles pass by the source several times because of large scale convection in the work chamber.
Thus there are serious consequences for the coalescence rate due to gravity driven convection. Concentrating the particles from an expanding 4 pi solid angle spatial distribution into a narrow rising plume causes the number of particles per unit volume in the plume to be increased. The particle collision rate is thus greatly increased, as can be seen from equation (1).